Render Image is further back than viewport image
In this first image, you can see a dark grey border around the plane and torus. Is border represents the edges of the render camera's view. I don't see this in your top image, which leads me to believe you're zoomed in like the second image. Notice in this view the camera has not moved, that is, both pictures will render the same, but you can no longer see the safe area because you have 'zoomed in' on the render area.
To see the whole render area press Home.